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represents a single photometric object, i.e. NP**—1 for each i. | represents a single photometric object, i.e. $N_i^{\rm phot}=1$ for each $i$. |
In this case photometric objects that have some overlap with the spectroscopic bin of interest are included in the sum and photometric objects with zero overlap have zero weight. | In this case photometric objects that have some overlap with the spectroscopic bin of interest are included in the sum and photometric objects with zero overlap have zero weight. |
Treating the photometric objects individually, rather than in an ensemble, removes the need for any arbitrary binning and effectively reduces the extension of the ensemble PDF along the line-of-sight and should thus significantly improve the clustering signal-to-noise. | Treating the photometric objects individually, rather than in an ensemble, removes the need for any arbitrary binning and effectively reduces the extension of the ensemble PDF along the line-of-sight and should thus significantly improve the clustering signal-to-noise. |
Because the weights in Eq. (6)) | Because the weights in Eq. \ref{eqn:wpvarweight}) ) |
are o;?=NP?f? a rough determination of how much this new estimator will improve the signal-to-noise of a w, estimate over existing methods, which only consider objects that have a peak photometric redshift in the bin of interest iswhere the { subscripts represent our new optimal estimator for a slice containing N?"°t photometric objects and the n represents the number of photometric objects with a PDF peak in the spectroscopic bin of interest. | are $\sigma_i^{-2} = N_i^{\rm phot} f_i^2$ a rough determination of how much this new estimator will improve the signal-to-noise of a $w_p$ estimate over existing methods, which only consider objects that have a peak photometric redshift in the bin of interest iswhere the $i$ subscripts represent our new optimal estimator for a slice containing $N^{\rm phot}$ photometric objects and the $n$ represents the number of photometric objects with a PDF peak in the spectroscopic bin of interest. |
The f; are the comoving fractional photometric redshift overlaps for objects in slice i and (f(x.)) is the same for the ensemble of photometric objects with a peak photometric redshift in the spectroscopic bin of interest. | The $f_i$ are the comoving fractional photometric redshift overlaps for objects in slice $i$ and $\langle
f(\chi_\star)\rangle$ is the same for the ensemble of photometric objects with a peak photometric redshift in the spectroscopic bin of interest. |
This is illustrated in Figure 2,, in which the upper panel plots the ensemble of the (n= 110410) PDFs with 1.8<Zpeak2.2. | This is illustrated in Figure \ref{fig:chibin}, , in which the upper panel plots the ensemble of the $n=110410$ ) PDFs with $1.8 < z_{\rm peak} < 2.2$. |
This ensemble has an (f(x.))=1.26x1073hMpc overlap with the true range 1.8«z2.2. | This ensemble has an $\langle f(\chi_\star)\rangle=1.26\times10^{-3}\invMpch$ overlap with the true range $1.8 < z < 2.2$. |
The lower panels plot! three individual (i.e. phot—NPhet 1) PDFs and their overlaps with 1.8<z<2.2. | The lower panels plot three individual (i.e. $N_1^{\rm phot}=N_2^{\rm phot}=N_3^{\rm phot}=1$ ) PDFs and their overlaps with $1.8 < z < 2.2$. |
In§ refsec:qsoresults,, we illustrate the degree to which our optimal estimator can improve clustering estimates for a “typical” analysis, using a sample of spectroscopic and photometric QSOs. | In \\ref{sec:qsoresults}, we illustrate the degree to which our optimal estimator can improve clustering estimates for a “typical” analysis, using a sample of spectroscopic and photometric QSOs. |
QSOs may be particularly well suited to our estimator as they are rare enough that their clustering is dominated by Poisson noise (e.g., see Figure 4)) out to reasonably large scales and f(x) is quite broad. | QSOs may be particularly well suited to our estimator as they are rare enough that their clustering is dominated by Poisson noise (e.g., see Figure \ref{fig:bootstrap}) ) out to reasonably large scales and $f(\chi)$ is quite broad. |
We note, though, that our optimal estimator should improve the signal-to-noise for any photometric clustering analysis. | We note, though, that our optimal estimator should improve the signal-to-noise for any photometric clustering analysis. |
The exact methodology we use in practice is as follows. | The exact methodology we use in practice is as follows. |
Eq (6)) can be rewritten as where and we have used w,=wo/ fi. | Eq \ref{eqn:wpvarweight}) ) can be rewritten as where and we have used $w_p=w_\theta/f_i$ . |
Now, consider substituting Eq. (1)), | Now, consider substituting Eq. \ref{eq:wtheta_DDDR}) ), |
thetypical DD/DR estimator for w(), into Eq. (8)) | thetypical $DD/DR$ estimator for $w(\theta)$ , into Eq. \ref{eqn:cweight}) ) |
where the the transverse separation, R, is evaluated using the | where the the transverse separation, $R$ , is evaluated using the |
(K=5.58mmag) and BD-0333826 (K=6.70mmag). | mag) and 3826 mag). |
We used the temperature reddening from ? to convert to L’, and scaled the magnitude with respect to the relative flux observed on both calibrator and science star: 992933 is 1.09+0.03 times brighter than 992945, and 33826 is 1.11+0.05 times brighter than 1141569. | We used the temperature reddening from \citet{2000asqu.book..143T} to convert to L', and scaled the magnitude with respect to the relative flux observed on both calibrator and science star: 92933 is $1.09\pm 0.03$ times brighter than 92945, and 3826 is $1.11\pm0.05$ times brighter than 141569. |
As a result, we estimated the L' magnitude of 992945 to be 5.58mmag and 1141569 to be mmag. | As a result, we estimated the L' magnitude of 92945 to be mag and 141569 to be mag. |
We checked that these values are roughly compatible with the magnitude derived solely by using the isochrones for pre-main sequence stars (?) giving 5.6 and 6.3mmag, respectively. | We checked that these values are roughly compatible with the magnitude derived solely by using the isochrones for pre-main sequence stars \citep{2000A&A...358..593S} giving 5.6 and mag, respectively. |
Scaling the brightness to derive the absolute magnitude at lO0ppc (assuming distances stated in Sect. 4.1)), | Scaling the brightness to derive the absolute magnitude at pc (assuming distances stated in Sect. \ref{targets}) ), |
we obtained My, mmag 992945) and Mjy,;—1.76 mmag 1141569). | we obtained $_{\rm L'}$ mag 92945) and $_{\rm L'}$ mag 141569). |
Thus, the 56 upper limits correspond to a nondetection of up to a absolute magnitude of Μι,= 10.4mmag for 992945 and My;= 7.6mmag_ for 1141569. | Thus, the $5\,\sigma$ upper limits correspond to a nondetection of up to a absolute magnitude of $M_{\rm L'}=10.4$ mag for 92945 and $M_{\rm L'}=7.6$ mag for 141569. |
To convert our detection limits to planetary masses limits, we usedDUSTY evolutionary models (?) convolved with the NaCo filters. | To convert our detection limits to planetary masses limits, we used evolutionary models \citep{2000ApJ...542..464C} convolved with the NaCo filters. |
Towards 992945, the models put a limit on the mass of a companion to 18 aat a separation of (A/D). | Towards 92945, the models put a limit on the mass of a companion to 18 at a separation of $\lambda/D$ ). |
Towards 1141569, the models limit the mass of a companion to 22 aatau.. | Towards 141569, the models limit the mass of a companion to 22 at. |
We have shown that aperture masking gives detection limits of the order of AL/mag—6, with an inner working angle close to A/2D. These results confirm previous detection limits obtained by the same aperture masking technique on the Keck telescope (??) In terms of scientific impact, this observational domain is important because it corresponds to a few astronomical units at a hundred parsec, the distance where the closest formation regions are. | We have shown that aperture masking gives detection limits of the order of $\Delta~{\rm L'\,mag}=6$, with an inner working angle close to $\lambda$ /2D. These results confirm previous detection limits obtained by the same aperture masking technique on the Keck telescope \citep{2011ApJ...731....8K,2011ApJ...730L..21H} In terms of scientific impact, this observational domain is important because it corresponds to a few astronomical units at a hundred parsec, the distance where the closest formation regions are. |
The scientific importance of this parameter space is highlighted by T Cha b detected by the same technique (?).. | The scientific importance of this parameter space is highlighted by T Cha b detected by the same technique \citep{2011A&A...528L...7H}. |
Simulations of the older debris disk tend to show that a magnitude or two in dynamic range is still needed to observe disk shaping planets. | Simulations of the older debris disk tend to show that a magnitude or two in dynamic range is still needed to observe disk shaping planets. |
Considering 1141569, for example, ? show that the disk geometry could be best modeled by a flyby star and a planet of a few Jupiter masses. | Considering 141569, for example, \citet{2009A&A...493..661R} show that the disk geometry could be best modeled by a flyby star and a planet of a few Jupiter masses. |
For these kinds of objects, a detection limit of two Jupiter masses would require a precision on the closure phases of 0.01 degree, something only possible if we understand how to precisely account for the systematics errors. | For these kinds of objects, a detection limit of two Jupiter masses would require a precision on the closure phases of 0.01 degree, something only possible if we understand how to precisely account for the systematics errors. |
'This paper has to be considere along with other direct detection techniques. | This paper has to be considere along with other direct detection techniques. |
In the case of ? ? | In the case of \citet{2007ApJS..173..143B}
\citet{2007ApJ...670.1367L} |
during Cycles 16 aud 21. ice. iu a gap of about 5 ceveles. may be relaed to a 555 vear cvele im solar activity (Yoshimura&Kambry1993:Javaraiah2008). | during Cycles 16 and 21, i.e., in a gap of about 5 cycles, may be related to a 55 year cycle in solar activity \citep{yk93,jj08}. |
. The value (it is oulv 0.08) of the cocfhicient of he correlation between the sunspot activity (amplitude of the evele) aud the slope is found to be negligible. | The value (it is only 0.08) of the coefficient of the correlation between the sunspot activity (amplitude of the cycle) and the slope is found to be negligible. |
During the 90-vear cycle (Cleissbere cevcle) im the sunspot activity there are many relatively stall time-scale strong fiations. whereas there are no such fluctuations during the 90-vear cycle in the slope. | During the 90-year cycle (Gleissberg cycle) in the sunspot activity there are many relatively small time-scale strong fluctuations, whereas there are no such fluctuations during the 90-year cycle in the slope. |
However. there is a close agreement in the epochs of the maxima and the miniunua of these eveles of the slope and the cycle amplitude (the phase shift between these is not clear iu Fig. [)). | However, there is a close agreement in the epochs of the maxima and the minima of these cycles of the slope and the cycle amplitude (the phase shift between these is not clear in Fig. \ref{fig4}) ). |
This may suggest the existence of a relationship between the long-term, variations iu the slope aud tje sunspot activity. | This may suggest the existence of a relationship between the long-term variations in the slope and the sunspot activity. |
Fi | Fig. |
e.o 6 shows the variations in the slope ai the correlation coeffcieut determiued from the data im year MTIs 1187G. στη, 22017. | \ref{fig6} shows the variations in the slope and the correlation coefficient determined from the data in 3-year MTIs 1876, 1877, ...., 2011. |
In order to check the solar ceveles tren* Il these parameters. iu this figure we lave also shown the variationiu the iuteruational suuspot umber smootlie by taking 3-vear ruuniug average. | In order to check the solar cycles trends in these parameters, in this figure we have also shown the variation in the international sunspot number smoothed by taking 3-year running average. |
Onlv a few of these values ofthe slopes shown in this figure are statistically insiemificaut. | Only a few of these values of the slopes shown in this figure are statistically insignificant. |
That is. in mauv intervals the values of κ are found to be insignificant at level. ancl the Student's “ft tests supgeest that the significant levels of the correspouding values of the correlation coefficieu are also good (Note: the big jump of the correlation cocfiicicnt from the interval 1977 to 1978 (the high values frou, LOTS onward) could be just an artifac of the multiplication of the area values of the SOON data with 1.1. in order to have a coniuuous and homogencous data for the whole period 22011 (cf. | That is, in many intervals the values of $\chi^2$ are found to be insignificant at level, and the Student's `t' tests suggest that the significant levels of the corresponding values of the correlation coefficient are also good (Note: the big jump of the correlation coefficient from the interval 1977 to 1978 (the high values from 1978 onward) could be just an artifact of the multiplication of the area values of the SOON data with 1.4, in order to have a continuous and homogeneous data for the whole period 2011 (cf., |
Sec; | Sec. |
2). | 2). |
As can be seen Fie. 6(( | As can be seen Fig. \ref{fig6}( ( |
a) the values of the slopes are cousiderably low near the declining ends of s1alb eveles (12. 16 and 23). particularly in the eu of Cycle 23 the slope is s1uallest im the last abou 100 vears (which iuav be related to the παπααν low and prolonged recent activity mininimn). | a) the values of the slopes are considerably low near the declining ends of small cycles (12, 16 and 23), particularly in the end of Cycle 23 the slope is smallest in the last about 100 years (which may be related to the unusually low and prolonged recent activity minimum). |
The loue-terii (90-vear evele) variation seen in the evcle-to-evcle variation (Fig. [)) | The long-term (90-year cycle) variation seen in the cycle-to-cycle variation (Fig. \ref{fig4}) ) |
cau also be secu in Fie. σ | can also be seen in Fig. \ref{fig6}( ( |
α). | a). |
We have used the 3-AITIs for the sake of better statistics. but the aforementioned patterus is also seen in the vearly data (figure is not shown here). iu spite of the laree uucertaimties in the vearly values. | We have used the 3-MTIs for the sake of better statistics, but the aforementioned patterns is also seen in the yearly data (figure is not shown here), in spite of the large uncertainties in the yearly values. |
Fie. | Fig. |
7 shows the plots of the mean slope values iu S-METTISies the data shown in Fig. 6(( | \ref{fig7} shows the plots of the mean slope values in 3-MTIs–i.e., the data shown in Fig. \ref{fig6}( ( |
a) versus the vear of the solar cvcles. 221 (data are available ouly for four vears of Cycle 11 aud ouly for 3 vears of Cycle 21). | a)–versus the year of the solar cycles, 24 (data are available only for four years of Cycle 11 and only for 3 years of Cycle 24). |
As can be seen in this figure. the pattern of the mean variation of the slope (the closed circle-solid curve) suggestsCoco a shelt increasing treud duniug the rising phases and a slight decreasing trend during the decay phases of a majority of the solar evcles. | As can be seen in this figure, the pattern of the mean variation of the slope (the closed circle-solid curve) suggests a slight increasing trend during the rising phases and a slight decreasing trend during the decay phases of a majority of the solar cycles. |
However. the overall spread in the data points is vorv lare particularly in the beeimuines aud the eudiues of the evcles. | However, the overall spread in the data points is very large, particularly in the beginnings and the endings of the cycles. |
That is. the variations during the different solar evcles highly differ from the mean pattern. mdicatiug the z ll-vear periodicity is very woeak/abseut iu the slope. | That is, the variations during the different solar cycles highly differ from the mean pattern, indicating the $\approx$ 11-year periodicity is very weak/absent in the slope. |
Overall we find that the relationship |Dy1,4| and AA, yds reasonably consistent and reliable even im the cases of the relatively siiall samples. | Overall we find that the relationship $|D_{\rm n-1, n}|$ and $A_{\rm n-1}$ is reasonably consistent and reliable even in the cases of the relatively small samples. |
It may be worth to note here that the average size of the spot eroups considerably varies duriug a cycle. | It may be worth to note here that the average size of the spot groups considerably varies during a cycle. |
It also differs frou evcle-to-cvcle. | It also differs from cycle-to-cycle. |
Therefore. the temporal variation im the slope of the Huear relationship may be mainly due to the dependence of the decay rate on the size/litetime of the spot groups. | Therefore, the temporal variation in the slope of the linear relationship may be mainly due to the dependence of the decay rate on the size/lifetime of the spot groups. |
We repeated all the above caleulatious for erowth rate. | We repeated all the above calculations for growth rate. |
The correlation between the erowth rate. Gy,4,4. the corresponding μα. is found to be low. r= 0.39. for the whole period data (wilL 60087 points). | The correlation between the growth rate, $G_{\rm n-1, n}$, and the corresponding $A_{\rm n-1}$ is found to be low, $r= 0.39$ , for the whole period data (with 60087 points). |
But it is stil found to be statistically siguificaut from the above used al the significance tests Gt should be noted that the values of n is different for the growth al clecay rates). | But it is still found to be statistically significant from the above used all the significance tests (it should be noted that the values of n is different for the growth and decay rates). |
However. the correlation deermincd from the data of an individual evele is found to be still samall and statistically insignificant. | However, the correlation determined from the data of an individual cycle is found to be still small and statistically insignificant. |
Thus. the relationship between Gy,44, and ly4 is considerably inconsistent. | Thus, the relationship between $G_{\rm n-1, n}$ and $A_{\rm n-1}$ is considerably inconsistent. |
ence. it is not shown here. | Hence, it is not shown here. |
There is also a considerable spread in Figs. | There is also a considerable spread in Figs. |
3 and I. | 3 and 4. |
Therefore. eventhe relatiouship between 124,4, aud 21,1 found above. is ouly sugeestive rather than compelling. | Therefore, even the relationship between $|D_{\rm n-1, n|}$ and $A_{\rm n-1}$ found above, is only suggestive rather than compelling. |
We analysed a large and reliable suuspot eroup data and found that the total amounts of growth and decay of spot eroups whose life times =2 davs in a eiven time iuterval (sav one-vear) well correlate to the zinouut of activity in the same interval. | We analysed a large and reliable sunspot group data and found that the total amounts of growth and decay of spot groups whose life times $\ge 2$ days in a given time interval (say one-year) well correlate to the amount of activity in the same interval. |
We have also found that there exist a reasonably good correlation | We have also found that there exist a reasonably good correlation |
a reference DPH together with à group of nearly co-aligned DPHs. having ROLL angles within | aremin of the reference one. as well as pointing offsets (in R.A. and Dec.) within 7 aremin of the reference one. | a reference DPH together with a group of nearly co-aligned DPHs, having ROLL angles within 1 arcmin of the reference one, as well as pointing offsets (in R.A. and Dec.) within 7 arcmin of the reference one. |
Then. each of the selected DPH rows was summed to the reference one. obtaining stacked DPH pairs. each being characterized by a “pointing offset” ranging from 0 to 7 arcmin. | Then, each of the selected DPH rows was summed to the reference one, obtaining stacked DPH pairs, each being characterized by a “pointing offset” ranging from 0 to 7 arcmin. |
For each of such stacked pairs. we performed a spectral analysis and we extracted the Crab flux. to be compared with the one obtained from the reference DPH. | For each of such stacked pairs, we performed a spectral analysis and we extracted the Crab flux, to be compared with the one obtained from the reference DPH. |
Details on the handling of different attitude files for the construction and analysis of a pair are given in Appendix AppendixB:.. | Details on the handling of different attitude files for the construction and analysis of a pair are given in Appendix \ref{Aspect}. |
The resulting flux-losses with respect to the reference DPH. as a function of the offset. for different coded fractions. are given in Table 5.. | The resulting flux-losses with respect to the reference DPH, as a function of the offset, for different coded fractions, are given in Table \ref{table_offset}. |
Although our investigation is far from complete. results suggest that significant flux losses (> 550)) may occur. especially for target position at low coded fractions. when stacking different DPHs with a pointing offset larger than 2 arcmin. | Although our investigation is far from complete, results suggest that significant flux losses $>$ ) may occur, especially for target position at low coded fractions, when stacking different DPHs with a pointing offset larger than 2 arcmin. |
Thus. we decided conservatively to stack DPHs only if their pointings are within 1.5 aremin. | Thus, we decided conservatively to stack DPHs only if their pointings are within 1.5 arcmin. |
Having assessed the overall correctness and reliability of our procedure on the bright Crab. we will proceed with the study of the microquasar GRO J1655-40. à source definitely fainter than the Crab and one known to be strongly variable. both in flux and in spectral shape. | Having assessed the overall correctness and reliability of our procedure on the bright Crab, we will proceed with the study of the microquasar GRO J1655-40, a source definitely fainter than the Crab and one known to be strongly variable, both in flux and in spectral shape. |
GRO J1655-40 had a large outburst in 2005. | GRO J1655-40 had a large outburst in 2005. |
Such an event started in the middle of February (it was discovered on February 17.99 during Galactic bulge seans with the RXTE/PCA instrument (?))) and lasted for more than 9 months. | Such an event started in the middle of February (it was discovered on February 17.99 during Galactic bulge scans with the RXTE/PCA instrument \citep{Markwardt_2005_GRO}) ) and lasted for more than 9 months. |
In what follows we shall take advantage of a very large database serendipitously collected by the BAT instrument during the whole outburst event as well as of the systematic monitoring performed by the RXTE satellite. | In what follows we shall take advantage of a very large database serendipitously collected by the BAT instrument during the whole outburst event as well as of the systematic monitoring performed by the RXTE satellite. |
This will allow us to compare our BAT results with quasi-simultaneous results obtained with the well calibrated instruments on-board RXTE. | This will allow us to compare our BAT results with quasi-simultaneous results obtained with the well calibrated instruments on-board RXTE. |
Such a cross-check will yield a very robust assessment of the capabilities of our analysis method as well as of the potentialities of BAT as a monitor for a (relatively) bright. strongly variable source. | Such a cross-check will yield a very robust assessment of the capabilities of our analysis method as well as of the potentialities of BAT as a monitor for a (relatively) bright, strongly variable source. |
All BAT observations covering the field of GRO J1655-40. collected between 2005/01/22 and 2005/11/11. were retrieved. | All BAT observations covering the field of GRO J1655-40, collected between 2005/01/22 and 2005/11/11, were retrieved. |
The complete dataset includes 796 observations. for a total of 8724 DPHs. corresponding to ~2.6 Ms observing time. | The complete dataset includes 796 observations, for a total of 8724 DPHs, corresponding to $\sim$ 2.6 Ms observing time. |
All the data analysis was performed by our automatic pipeline. | All the data analysis was performed by our automatic pipeline. |
As a first step. good data are selected. according to the prescription deseribed in Appendix Α.Ι... | As a first step, good data are selected, according to the prescription described in Appendix \ref{Preliminary_data_selection_and_preparation}. |
A total of 2080 (~24%)) DPHs were discarded after data screening. | A total of 2080 $\sim$ ) DPHs were discarded after data screening. |
Such a percentage is compatible with that found for the Crab dataset in section ??.. | Such a percentage is compatible with that found for the Crab dataset in section \ref{Crab_results}. |
Nest. well-aligned. contiguous DPHs are combined up to a maximum integration time of | hour. | Next, well-aligned, contiguous DPHs are combined up to a maximum integration time of 1 hour. |
As a result. we obtained 1650 merged DPHs. | As a result, we obtained 1650 merged DPHs. |
Then. from each data block. a spectrum is extracted with the mask-weighting technique. and the appropriate response matrix is produced. | Then, from each data block, a spectrum is extracted with the mask-weighting technique, and the appropriate response matrix is produced. |
An automatic spectral analysis is then carried. out in XSPEC. | An automatic spectral analysis is then carried out in XSPEC. |
After evaluating the source signal-to-noise. spectra with no signal (S/N=O)were discarded. | After evaluating the source signal-to-noise, spectra with no signal (S/N=0)were discarded. |
This resulted in the rejection of 378 spectra (~ of the total). | This resulted in the rejection of 378 spectra $\sim$ of the total). |
Low S/N spectra (with source detection below ~Ia level) are used to set ar upper limit to the source flux. | Low S/N spectra (with source detection below $\sim4\sigma$ level) are used to set an upper limit to the source flux. |
Contiguous. low-S/N spectra are summed. as well as their response matrices. in an attempt to increase the statistics. and the spectral analysis repeated on such combined spectra. | Contiguous, low-S/N spectra are summed, as well as their response matrices, in an attempt to increase the statistics, and the spectral analysis repeated on such combined spectra. |
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